document.write( "Question 849306: An infinite geo series has the sum 16. If the sum of the first two terms is 15, find a1 and r
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Algebra.Com's Answer #511693 by AnlytcPhil(1807)\"\" \"About 
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An infinite geo series has the sum 16.
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document.write( "\"S%5Binfinity%5D\"\"%22%22=%22%22\"\"a%5B1%5D%2F%281-r%29\"\r\n" );
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document.write( "\"a%5B1%5D%2F%281-r%29\"\"%22%22=%22%22\"\"16\"\r\n" );
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document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%281-r%29\"\r\n" );
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\n" ); document.write( "the sum of the first two terms is 15
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document.write( "\"a%5B2%5D\"\"%22%22%2B%22%22\"\"a%5B1%5D\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "\"a%5B2%5D\"\"%22%22%2B%22%22\"\"a%5B1%5D%2Ar\"\r\n" );
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document.write( "\"a%5B1%5D%2Ar\"\"%22%22%2B%22%22\"\"a%5B1%5D\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "\"a%5B1%5D%28r%2B1%29\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "\"system%28a%5B1%5D=16%281-r%29%2C+a%5B1%5D%28r%2B1%29=15%29\"\r\n" );
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document.write( "Use substitution:\r\n" );
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document.write( "\"16%281-r%29%28r%2B1%29\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "\"16%28r%2B1-r%5E2-r%29\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "\"16%281-r%5E2%29\"\"%22%22=%22%22\"\"15\" \r\n" );
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document.write( "\"16-16r%5E2\"\"%22%22=%22%22\"\"15\"\r\n" );
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document.write( "\"-16r%5E2\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "\"r%5E2\"\"%22%22=%22%22\"\"1%2F16\"\r\n" );
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document.write( "\"r\"\"%22%22=%22%22\"\"%22%22+%2B-+1%2F4\"\r\n" );
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document.write( "using \"r=1%2F4\"\r\n" );
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document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%281-1%2F4%29\"\r\n" );
document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%283%2F4%29\"\r\n" );
document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"12\"\r\n" );
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document.write( "using \"r=-1%2F4\"\r\n" );
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document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%281-%28-1%2F4%29%29\"\r\n" );
document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%281%2B1%2F4%29\"\r\n" );
document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"16%285%2F4%29\"\r\n" );
document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"20\"\r\n" );
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document.write( "Two solutions:\r\n" );
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document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"12\", \"r=1%2F4\"\r\n" );
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document.write( "and\r\n" );
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document.write( "\"a%5B1%5D\"\"%22%22=%22%22\"\"20\", \"r=-1%2F4\"\r\n" );
document.write( " \r\n" );
document.write( "Edwin
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